11.2.1 Describe what is meant by the Doppler Effect.
The Doppler effect is the name given to the change of perceived frequency of a wave as a result of the movement of the source or the movement of the observer.
From the frame of reference of the observer, if the source is moving towards the observer, then the frequency will increase. If the source is moving away, the frequency will decrease.
11.2.2 Explain the Doppler effect by reference to wavefront diagrams for moving-detector and moving-source situations.
The concept behind the Doppler effect is similar to velocity problems we used to do in elementary school, where two trains approach or travel away from each other.
When the source is stationary (figure 1), there is a constant velocity at which the wave travels away from the source (let this be Vw). This velocity is independent of the movement of the source.
figure 1: stationay source
The period of the wave (T) is also the intervals at which successive waves are emitted from the source. So the wavelength of the wave perceived by the observers is:
This wavelength is perceived to be different when the source of this wave begins to move (figure 2). The wave is still traveling away from the source at the same velocity and the source still emits the waves at the same intervals of time, but the the source is catching up with the wave.:
figure 2: moving source
This is the same concept as a train traveling away from a station compared to a train traveling away from another moving train traveling the same direction. In the latter instance, the relative velocity (and distance) between the two trains should be less.
The new perceived wavelength, depending on the location of the observer, is (let Vs be the velocity of the source) :
We can see that the new wavelength seems shorter to the observer the source is approaching, and longer for the observer that the source is moving away from. There will be a corresponding frequency change associated with the change in wavelength.
Here is a Java applet animation of the concept above:
Click here for an applet that shows how changes in the velocity of the source affect the Doppler effect.
11.2.3 & 11.2.4 Apply the Doppler effect equations for sound and solve problems on the Doppler effect for sound.
For a moving sound source, the new frequency can be calculated by (v = wave ; u = source):
For a moving observer, the new frequency can be calculated by (v = wave ; u = observer):
Both equations in the data booklet. Add the velocities if the wave and the observer/source are traveling in opposite directions. Subtract velocities if the wave and the observer/source are moving in the same direction.
Example: A train is moving towards the station at the speed of 2.8 m/s. On the station, a whistle of frequency 2000 Hz is blown. What is the frequency of the sound wave that is reflected from the train? Assume speed of sound to be 343 m/s.
There are two doppler effects occurring here. First, the train acts as a moving observer as the sound wave hits the train. Then the train acts as a moving source to reflect the sound waves.
As an observer, the train and the wave are moving in different directions so we add the velocities:
This perceived frequency is then reflected. As a source, the velocity of the reflected wave and the velocity of the train are in the same direction so we subtract the velocities:
So the reflected frequency is 2032 Hz. In reality, the incoming and reflected frequency will interfere. The difference between the two frequencies (32 Hz) will be heard. This is called the beat frequency.
11.2.5 Solve problems on the Doppler effect for electromagnetic waves using the approximation (delta f) = (v/c) f.
The Doppler equations for sound rely on finding the relative velocity between the wave and the source/observer. This is not possible for EM waves because EM waves have a constant velocity in any reference frame.
We can approximate the Doppler effect of EM waves using the following equation (assuming v << c):
11.2.6 Outline an example in which the Doppler effect is used to measure speed.
A speed sensor works by measuring the change in frequency of a wave caused by a moving object. The speed sensor always measures relative speed, or the speed of the object perceived from the sensor's point of reference (person measuring always at rest).
A wave of a specific frequency (ultrasonic in most devices) is transmitted at the moving object. The frequency of the wave is changed because of the Doppler effect (similar to example above). Then the resulting frequency is measured. The reflected frequency can be expressed as a combination of the two Doppler effect equations (v = speed of sound ; u = speed of object) :
Rearranging this equation for the speed of the object gives:
Note that if this value is positive, then the object is moving towards the sensor. If the value is negative, then it is moving away from the sensor.
11.2: The Doppler Effect
Objectives
Click to go to section11.2.1 Describe what is meant by the Doppler Effect
11.2.2 Explain the Doppler effect by reference to wavefront diagrams for moving-detector and moving-source situations.
11.2.3 & 11.2.4 Apply the Doppler effect equations for sound and solve problems on the Doppler effect for sound.
11.2.5 Solve problems on the Doppler effect for electromagnetic waves using the approximation (delta f) = (v/c) f.
11.2.6 Outline an example in which the Doppler effect is used to measure speed.
11.2.1 Describe what is meant by the Doppler Effect.
The Doppler effect is the name given to the change of perceived frequency of a wave as a result of the movement of the source or the movement of the observer.
From the frame of reference of the observer, if the source is moving towards the observer, then the frequency will increase. If the source is moving away, the frequency will decrease.
11.2.2 Explain the Doppler effect by reference to wavefront diagrams for moving-detector and moving-source situations.
The concept behind the Doppler effect is similar to velocity problems we used to do in elementary school, where two trains approach or travel away from each other.
When the source is stationary (figure 1), there is a constant velocity at which the wave travels away from the source (let this be Vw). This velocity is independent of the movement of the source.
The period of the wave (T) is also the intervals at which successive waves are emitted from the source. So the wavelength of the wave perceived by the observers is:
This wavelength is perceived to be different when the source of this wave begins to move (figure 2). The wave is still traveling away from the source at the same velocity and the source still emits the waves at the same intervals of time, but the the source is catching up with the wave.:
This is the same concept as a train traveling away from a station compared to a train traveling away from another moving train traveling the same direction. In the latter instance, the relative velocity (and distance) between the two trains should be less.
The new perceived wavelength, depending on the location of the observer, is (let Vs be the velocity of the source) :
We can see that the new wavelength seems shorter to the observer the source is approaching, and longer for the observer that the source is moving away from. There will be a corresponding frequency change associated with the change in wavelength.
Here is a Java applet animation of the concept above:
Click here for an applet that shows how changes in the velocity of the source affect the Doppler effect.
11.2.3 & 11.2.4 Apply the Doppler effect equations for sound and solve problems on the Doppler effect for sound.
For a moving sound source, the new frequency can be calculated by (v = wave ; u = source):
For a moving observer, the new frequency can be calculated by (v = wave ; u = observer):
Both equations in the data booklet. Add the velocities if the wave and the observer/source are traveling in opposite directions. Subtract velocities if the wave and the observer/source are moving in the same direction.
Example: A train is moving towards the station at the speed of 2.8 m/s. On the station, a whistle of frequency 2000 Hz is blown. What is the frequency of the sound wave that is reflected from the train? Assume speed of sound to be 343 m/s.
There are two doppler effects occurring here. First, the train acts as a moving observer as the sound wave hits the train. Then the train acts as a moving source to reflect the sound waves.
As an observer, the train and the wave are moving in different directions so we add the velocities:
This perceived frequency is then reflected. As a source, the velocity of the reflected wave and the velocity of the train are in the same direction so we subtract the velocities:
So the reflected frequency is 2032 Hz. In reality, the incoming and reflected frequency will interfere. The difference between the two frequencies (32 Hz) will be heard. This is called the beat frequency.
11.2.5 Solve problems on the Doppler effect for electromagnetic waves using the approximation (delta f) = (v/c) f.
The Doppler equations for sound rely on finding the relative velocity between the wave and the source/observer. This is not possible for EM waves because EM waves have a constant velocity in any reference frame.
We can approximate the Doppler effect of EM waves using the following equation (assuming v << c):
11.2.6 Outline an example in which the Doppler effect is used to measure speed.
A speed sensor works by measuring the change in frequency of a wave caused by a moving object. The speed sensor always measures relative speed, or the speed of the object perceived from the sensor's point of reference (person measuring always at rest).
A wave of a specific frequency (ultrasonic in most devices) is transmitted at the moving object. The frequency of the wave is changed because of the Doppler effect (similar to example above). Then the resulting frequency is measured. The reflected frequency can be expressed as a combination of the two Doppler effect equations (v = speed of sound ; u = speed of object) :
Rearranging this equation for the speed of the object gives:
Note that if this value is positive, then the object is moving towards the sensor. If the value is negative, then it is moving away from the sensor.
Sources
Figure 1 & Figure 2: Physics (Giancoli) 5th Edition, Prentice HallDoppler Java Applet: W. Fendt (http://www.walter-fendt.de/ph14e/index.html)
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